Download Algebra M-2 - Garnet Valley

Algebra M-2
Final Exam Review
Name
Date
Part One: Multiple Choice. Choose the letter of your answer choice and circle it.
Show your work on this paper or on a separate piece of paper.
1)
2)
Solve the linear system
-2x + 7y = -3
x – 7y = -2
A)
(-1, -5)
B)
None
(-2, 0)
B) Exactly One
(1, 5)
D)
(5, 1)
C)
2x 4 y 5
D)
(10,10)
C) Infinitely Many
D)
Two
B)
49 28
8y
x2
4x – 2y = 6
2x – y = 3
7 28
C)
49 11
D)
2x 4 y 6
C)
4x 4 y 6
D) 4 x 4 y 9
2x y 
2
3 2
B)
Simplify and rewrite with positive exponents:
A)
(4, 5)
74  77
7 11
Simplify
A)
6)
(-5, -8)
Simplify
A)
5)
C)
How many solutions does the linear system have?
A)
4)
B)
Which point lies on the graph of the linear system: 5x – 6y = -10
-15x + 14y = 10
A)
3)
(-1, 5)
B)
8y
x3
C)
4 x
3
6y3
x2

y 3 2 y 2

D)
6
x3 y
7)
A)
8)
1
x7
C)
x3
C)
0.00212
D)
C)
3.6 x 10-7
D) 3.6 x 10-6
D)
212
B)
2,120
2.12
3.6 x 107
B)
3.6 x 106
x2 – 9 = 6x
B)
2x2 + x - 1 = 0
C)
5x –3x2 = 0
Solve 3x2 – 78 = 114
A)
12)
x7
Which quadratic equation is written in standard form?
A)
11)
B)
Rewrite 36,000,000 in scientific notation
A)
10)
1
x3
Rewrite 2.12 x 10-3 in decimal form
A)
9)
x 2
x5
Evaluate
2 3
Simplify
A)
B)
6
C)
4 3
D)
8
B)
3 6
C)
2 27
D)
3 12
54
6 3
13) What is the x-coordinate of the vertex of the graph of the equation y = -2x2 - x + 8?
A)
14)
15)
-1
B)
½
1
4
C)

C)
0 and 4
D)
1
4
What are the solutions of x2 + 6x – 40 = 0
A)
-10 and 4
B)
-4 and 10
Add
(-x2 – 5x + 7) + (-7x2 + 5x – 2)
A)
-8x2 + 5
B)
-8x2 + 10x + 5
C)
6x2 + 5
D)
-8x2 - 10x + 5
D) 4 and 10
5x
16)
Subtract
A)
7x3 + 3x2 - 2x + 6
D)
3x3 + 3x2 – 2x + 6
17)
Multiply
3
 
B)
B)
-6x4 + 12x2 + 8x2
C)
-6x4 + 12x3 + 8x2
D)
-3x4 + 15x3 + 21x2
(4x – 1)(5x - 2)
20x2 – 5x +2 B)
19)
Multiply
(2x – 9)2
A)
4x2 + 81
B)
D)
4x2 – 36x + 81
20)
Factor x2 -2x – 120
A)
20x2 -13x +2 C)
4x2 – 18x + 81
(x -12)(x + 10)
B)
Solve the equation by factoring:
A)
2, -2
B)
4, -1
20x2 – 3x – 2 D)
C)
20x2 – 8x - 2
4x2 + 36x +81
(x + 12)(x – 10)
C)
(x – 6)(x + 20)
x2 - 4x = -4
C)
2
D)
4
Factor 2x2 – 50
A)
2(x + 5)(x – 5)
B)
(2x + 5)(x – 5)
C)
(x + 5)(x – 5)
B)
(2x + 1)(x – 8)
C) (2x -1)(x + 8)
Factor 2x2 + 15x – 8
A)
24)
3x3 + 3x2 – 2x – 6
12x3 – 3x4 + 8x2
A)
23)
C)
A)
Multiply
22)
3x3 + 3x2 – 2x – 4
2x2(6x – 3x2 + 4)
18)
21)

 3x 2  x  1  2 x 3  x  5
(2x – 8)(x + 1)
What is the greatest common factor of 5x2yz + 10xz?
A)
xz
B)
5x2z
C)
5x2
D)
5xz
25)
Solve the proportion
A)
26)
-82
4
6

y 9 y  7
B)
-41
C)
D)
41
D)
y
Write the equation if x and y vary directly when x = 9 and y = 36
A)
y = 4x
B)
y = -4x
Simplify
x 3  10 x 2  9 x
x 2  5x  6
A)
x9
x6
B)
28)
What is the least common denominator of
A)
x
29)
What is the domain of the function
A)
B)
x  5
Subtract
A)
2 7
x
x6
C)
x+2
B)
y
C)
27)
30)
7
C)
324
x
x
( x  1)( x  6)
1
,
x
D)
x ( x  9)
x6
2
, 3
x2
x(x+2)
D)
3x(x+2)
y x5
x  5
C)
x5
D)
5 7  175  63
B)
4
x
 7 7 C)
7 7
D)
13 7
x5
Part Two: Free Response. Show all work used to solve the problem. Circle your
answer.
31)
Solve the linear system by graphing:
4x – y = 3
3x + y = 4
32)
Solve the linear system using any method:
x + 9y = 9
3x + 6y = 6
2
33)
Simplify the following:
34)
Graph the quadratic equation:
 8 x 4 y  12 xy 3

 
2 
8x 8
 2y 
y = x2 – 5x + 4
35)
Solve the quadratic equation using the quadratic formula:
36)
Find the product
37)
Multiply
x 2  16 3x  9 x 2
 2
3x 3
x  5x  4
39)
Subtract
6x
5x  4

x 4
x 4
41)
Solve the equation
3x2 – 4x + 1 = 0
(x + 3)(2x2 – x - 10)
2x 1 1
 
9
x 3
38) Divide
40)
Add
x 2  9x  8
 ( x  1)
x 8
x4 x6

2x
3x
42)
Graph the equation y  x  1
43)
Multiply
45)
Solve

6 2 34 2
x 35

44)
Simplify
2
3
46)
Solve
2x  3  2  3
47)
Use the Pythagorean theorem to find the hypotenuse of a right triangle if the legs
are 3 and 4
48)
What is the midpoint between (-3, -2) and (-6, 7)
49)
Find an expression for the area of a rectangle is the width is x – 2 and the length is
2x + 3
50)
Use a proportion to solve the problem:
If 8 books cost $3.20, then how much does 7 books cost?